1. Technical Field of the Invention
The present invention is directed to increasing the accuracy of the measurement of thermal expansion coefficients (CTE) performed on thin film samples. More specifically, in accordance with the present invention, the CTE increased measurement accuracy is obtained using any of the following procedures: (a) by measuring the baseline using the same set-up used in the measurement; (b) by identifying a correction factor; (c) by using specific, low expansion clamps; or (d) by extracting the CTE from measurements of samples with various lengths.
2. Description of the Related Art
The testing of plastics is generally carried out for the same reasons as apply to the testing of other materials, namely to determine their suitability for a particular application, for quality control purposes or to obtain a better understanding of their behavior under various conditions. It is necessary for a manufacturer to be able to measure its performance with relation to other materials and thus be in a position to assess the market likely to be available to it.
The physical testing of plastics must be standardized if the comparison of physical data from two or more different sources is to have any meaning. The physical testing of plastics can be classified generally as (a) dimensional; (b) thermal; (c) mechanical; (d) electrical; and (e) optical. The results of physical tests carried out on a material often depend upon the ambient conditions of temperature, humidity, the size, shape and method of preparation of the test pieces and the techniques of measurement employed.
Testing of the thermal properties of plastics is important to give the plastic user some idea of the range of safe temperatures at which the plastic can be used. Some of the important thermal properties are thermal conductivity, coefficient of thermal or linear expansion, specific heat, softening point, heat distortion temperature and mold shrinkage.
The present invention relates to accurately measuring the CTE as this test is now advantageously used to test thin samples of polymers such as polyimide, and to a lesser extent, epoxy resins used in computer applications.
CTE""s of materials are typically measured using a thermal mechanical analyzer (TMA). A TMA is an instrument used which is capable of measuring the displacement of a measuring probe with great accuracy in the compression mode, typical for CTE testing of rigid samples. The probe is in contact with a sample to be measured and detects changes in sample dimensions in probe direction and transmits results to a displacement detection unit. Test sample dimensions can change by the application of temperature or weight to the sample.
These dimensional changes may be time dependent. In the case of CTE measurements, the contact with the sample must be chosen so that the sample dimension does not change as a consequence of the probe; or if the sample dimension does change, such change is minimal and reproducible.
FIGS. 1A and 1B are generally equivalent with the exception that 1A operates in a compression mode, while 1B works in a tension mode such that the probe becomes the second sample holder. The sample in 1B is connected to the two holders by clamps shown in FIG. 3.
A typical TMA is depicted in FIG. 1A (prior art) comprising a probe (1), sample holder (2), heater (3), micrometer (4) (shown for illustrative purposes and not an essential part of a TMA), thermocouple (5), differential transformer (6), core (7), force generator (8). In a typical use, the plastic sample to be tested is held between sample holder (2) and probe (1). A force is applied to the sample, and the resulting changes in sample length are detected by the independently connected differential transformer (6) and core (7).
The TMA can be used in tensile mode for flexible samples pursuant to the present invention and is depicted in FIG. 1B (prior art). (Many identical elements are present in the structures depicted in FIG. 1A and FIG. 1B. To assist in an understanding of the structures of FIGS. 1A and 1B and to avoid confusion, the elements depicted in FIG. 1B which are also contained in FIG. 1A are indicated immediately after the numerical designation of the elements in FIG. 1B in brackets.) The unit comprises a load generator (10)(8), a core(11)(7), differential detector (12)(6), micrometer (13)(4), sample holder (14)(2), outer tube (15) not included in FIG. 1A, probe (16)(1), sample (17), and furnace (18)(3). The TMA module (19) receives a TMA/SS signal (20), a temperature signal from thermocouple (21) (5) and provides heater power (22). Also included in this apparatus is a means for processing software (23) used to provide certain instructions to the apparatus during operation as hereinafter described.
In this embodiment, with respect to the apparatus depicted in FIG. 1B, sample cylinder holder 14 is adjustably attached to differential transformer 12 via micrometer 13. When micrometer 13 is adjusted to an initial position, sample cylinder 14 is stationary with respect to detector 12. Probe 16 is connected to core 11 and sample 17. The top of probe (16) is also connected to a first end of balance arm (24). The other end of balance arm (24) is connected to electric load generator (10) which controls the load according to CPU guidance. The manner in which the force on the probe is generated is not relevant to the invention. There are a plurality of different ways that this may be accomplished. Differential detector (12) detects the movement of probe (16) as the sample (17) length changes, and outputs this as a TMA signal (20). Recorded signals are time, temperature, dimensional change and load.
There are a variety of probes that are used in the TMA depending upon what test is being conducted. The probes are configured for expansion, volume expansion, compression and penetration. In addition, accessories for tension and three point bending, and cubical are available. When combined with a dynamic loading program, a variety of applications not pertinent to this discussion are possible.
Presently, several ways of accomplishing contact of the probe to a sample exist. However, if the sample is a thin film, there is essentially only one way to guarantee continuous contact between the probe and the film while at the same time not bending the film.
In the method of the present invention, sample (30) is held by two clamps (31) and (32) as shown in FIGS. 2A and 2B (prior art front and side views respectively). FIGS. 2A and 2B show that top clamp (31) is held by or connected to probe (33) while bottom clamp (32) is stationary or fixed to stationary sample holder (34). Probe (33) and stationary sample holder support (34) are made from a material (such as quartz) which possesses a very small expansion coefficient so as not to interfere with the expansion of the sample.
Using the set up described above and depicted in FIGS. 2A and 2B, sufficient tensile force is applied to the probe so that the sample film (30) is under light tension. The length of the sample between the clamps (31) and (32) is recorded. For CTE measurements the sample is heated (cooled) and the probe displacement with temperature is measured.
FIG. 3 depicts a different side view of the elements depicted in FIG. 2B and includes a depiction of displacement sensor comprising calibrated measuring means (4) indicating one way in which measured displacement is determined. Elements (43) and (44) are made of a material with limited thermal expansion, such as quartz, and element (43) is subjected to a pulling force in direction (45). Distance L is the sample length. It is generally assumed that clamps (41) and (42), used to hold sample (40) do not contribute to the measured displacement. This is specifically stated in the user manual of one such instrument; (See: Seiko TMA Users Manual, Appendix-A, A-3).
FIG. 3 is identical to FIG. 2B with the exception that it adds a side view depiction of a graduated measurement scale 49 which indicates the extent of measured displacement.
A computer analysis software program collects displacement and temperature values. Often, time values are collected. Various software routines are used to extract and calculate the CTE for the particular sample tested. The CTE is computed as the difference of measured displacement D1, at temperature T1, and displacement D2, at temperature T2, divided by the difference between T1 and T2 and is exemplified by the expression: CTE =(D1xe2x88x92D2)/(T1xe2x88x92T2) [units of xc2x0 C.xe2x88x921]; wherein [D1xe2x88x92D2] is called the measured overall displacement (MD) (also referred to as (OD)); and T1xe2x88x92T2 is called the temperature range (xcex94T).
In order to obtain accurate values, the TMA must be well calibrated. This calibration includes collections of baselines and other instrument parameters which are conveniently incorporated into the software to obtain accurate data during measurements performed on samples.
In the electronics industry the matching of CTEs of dissimilar materials is of great importance because mismatch of the CTE of the various materials comprising an electronic device such as a memory or logic chip or an electronic package leads to stresses which influence the durability and performance of the device. Of particular importance is the measurement of materials with CTEs in the vicinity of the CTE of silicon (2.6 ppm/xc2x0 C.).
In order to provide for the demands of the electronic industry, the chemical industry has responded by synthesizing polymeric materials which exhibit CTEs that match the 2.6 ppm/xc2x0 C. value of silicon noted above. While silicon can be measured using compression mode CTE measurements, the CTE of these newly developed polymer films can only be measured directly in the tension mode. The reason for this is that in many polymer films, the CTE is a function of film thickness. Thus, thicker films which could be measured by other means will not give the required CTE values.
The thickness of the samples used in accordance with the present invention is in the range of between about 1 mm to 1 xcexcm, preferably between about 150 xcexcm and 5 xcexcm.
Laboratory measurements have established that CTEs measured with the above-described tension mode do not give accurate results. Errors for materials such as silicon, were off by as much as 480%, even with a well calibrated instrument. Errors varied with sample length.
It is an object of the present invention to provide a method which allows accurate measurements of the CTE of thin films using the tensile mode. In particular, the present invention describes methods using the tensile mode that allow accurate measurement of the CTE of films with low expansion coefficients, that is between about xe2x88x9225 and +50 ppm/xc2x0 C.
The predicate for the present invention is the discovery that in the course of determining the CTE of materials using a TMA, the clamps used in the TMA apparatus to hold the sample, contribute to the overall observed dimensional change of the sample. This dimensional change phenomenon is attributable to the fact that the clamps expand with heating and contract with cooling. The absolute values of the clamp displacement contribution to the overall value of the CTE of a sample is small. The accuracy of the CTE for samples with large CTE""s is therefore not greatly influenced by the clamp displacement contribution.
However, clamp displacement can be a considerable portion of the dimensional change observed for samples with small CTE""s. The present invention, as disclosed herein, eliminates, minimizes, or adjusts for the clamp expansion in order to obtain accurate CTE""s.
The present invention discloses a plurality of ways to eliminate the influence of clamp dimensional changes on the displacement measurement during the measurement of the CTE of samples in tension using the TMA apparatus.
In one embodiment, clamp dimensional changes are eliminated by making clamps from a material with a CTE close to zero.
In a second embodiment, clamp dimensional changes, i.e. expansion or contraction, during the process are accounted for by fabricating the clamps from a material with a known, fixed CTE, thereby eliminating the influence of the CTE of the clamp material. Additionally, the clamps can be fabricated from a material that possesses a CTE that is identical for heating and cooling.
In another embodiment, the clamps are fabricated from a material having a CTE that changes linearly in the range of operation. In this embodiment, actual clamp dimensional changes during the measurement procedure must be taken into account. This is achieved by subtracting a predetermined and prerecorded baseline (value) from the test measurement results. In another embodiment CTE measurement for various sample lengths are conducted and the slope of a straight line through points on a MD (measured displacement)/xcex94T (temperature range of displacement measurement) vs. sample length plot is obtained. The slope yields the corrected CTE.